A conventional system of the above described type is arranged to have a motor which provides auxiliary power used to assist in steering for a steering shaft of a rack steering gear via a speed reduction system by way of a transfer mechanism such as a gear or a belt.
However, the above described coventional system involves the problem that the motor generates excessive heat due to the considerable amount of current continuously flowing therethrough and this may in turn generate smoke or unpleasant smells from the motor and may eventually cause critical damage if the motor suffers from burning at such times as when the steering wheel is held for a long period of time at its extreme positions when fully rotated while the vehicle is stationary and when a lot of time is used in putting a car into a garage.